1.
Random variable
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In probability and statistics, a random variable, random quantity, aleatory variable, or stochastic variable is a variable quantity whose value depends on possible outcomes. It is common that these outcomes depend on physical variables that are not well understood. For example, when you toss a coin, the outcome of heads or tails depends on the uncertain physics. Which outcome will be observed is not certain, of course the coin could get caught in a crack in the floor, but such a possibility is excluded from consideration. The domain of a variable is the set of possible outcomes. In the case of the coin, there are two possible outcomes, namely heads or tails. Since one of these outcomes must occur, thus either the event that the coin lands heads or the event that the coin lands tails must have non-zero probability, a random variable is defined as a function that maps outcomes to numerical quantities, typically real numbers. In this sense, it is a procedure for assigning a numerical quantity to each outcome, and, contrary to its name. What is random is the physics that describes how the coin lands. A random variables possible values might represent the possible outcomes of a yet-to-be-performed experiment and they may also conceptually represent either the results of an objectively random process or the subjective randomness that results from incomplete knowledge of a quantity. The mathematics works the same regardless of the interpretation in use. A random variable has a probability distribution, which specifies the probability that its value falls in any given interval, two random variables with the same probability distribution can still differ in terms of their associations with, or independence from, other random variables. The realizations of a variable, that is, the results of randomly choosing values according to the variables probability distribution function, are called random variates. The formal mathematical treatment of random variables is a topic in probability theory, in that context, a random variable is understood as a function defined on a sample space whose outputs are numerical values. A random variable X, Ω → E is a function from a set of possible outcomes Ω to a measurable space E. The technical axiomatic definition requires Ω to be a probability space, a random variable does not return a probability. The probability of a set of outcomes is given by the probability measure P with which Ω is equipped. Rather, X returns a numerical quantity of outcomes in Ω — e. g. the number of heads in a collection of coin flips
2.
Opinion poll
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An opinion poll, sometimes simply referred to as a poll, is a human research survey of public opinion from a particular sample. Opinion polls are usually designed to represent the opinions of a population by conducting a series of questions, since Jackson won the popular vote in that state and the whole country, such straw votes gradually became more popular, but they remained local, usually city-wide phenomena. In 1916, The Literary Digest embarked on a national survey, then, in 1936, its 2.3 million voters constituted a huge sample, but they were generally more affluent Americans who tended to have Republican sympathies. The Literary Digest was ignorant of this new bias, the week before election day, at the same time, George Gallup conducted a far smaller survey, in which he polled a demographically representative sample. Gallup correctly predicted Roosevelts landslide victory, the Literary Digest soon went out of business, while polling started to take off. Elmo Roper was another American pioneer in political forecasting using scientific polls and he predicted the reelection of President Franklin D. Roosevelt three times, in 1936,1940, and 1944. Louis Harris had been in the field of opinion since 1947 when he joined the Elmo Roper firm. Looking for popular support or dissent with this question asked by appeasement politician, the Allied occupation powers helped to create survey institutes in all of the Western occupation zones of Germany in 1947 and 1948 to better steer denazification. By the 1950s, various types of polling had spread to most democracies, in long-term perspective, advertising had come under heavy pressure in the early 1930s. The Great Depression forced businesses to cut back on their advertising spending. Layoffs and reductions were common at all agencies, the New Deal furthermore aggressively promoted consumerism, and minimized the value of advertising. Historian Jackson Lears argues that By the late 1930s, though, George Gallup, the vice president of Young and Rubicon, and numerous other advertising experts, led the way. Moving into the 1940s, the played a leading role in the ideological mobilization of the American people for fighting the Nazis. As part of effort, they redefined the American Way of Life in terms of a commitment to free enterprise. Advertisers, Lears concludes, played a crucial role in creating the consumer culture that dominated post-World War II American society. Opinion polls for many years were maintained through telecommunications or in person-to-person contact, Methods and techniques vary, though they are widely accepted in most areas. Over the years, technological innovations have also influenced survey methods such as the availability of electronic clipboards, verbal, ballot, and processed types can be conducted efficiently, contrasted with other types of surveys, systematics, and complicated matrices beyond previous orthodox procedures. Opinion polling developed into popular applications through popular thought, although rates for some surveys declined
3.
Survey sampling
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In statistics, survey sampling describes the process of selecting a sample of elements from a target population to conduct a survey. The term survey may refer to different types or techniques of observation. In survey sampling it most often involves a questionnaire used to measure the characteristics and/or attitudes of people, different ways of contacting members of a sample once they have been selected is the subject of survey data collection. The purpose of sampling is to reduce the cost and/or the amount of work that it would take to survey the entire target population, a survey that measures the entire target population is called a census. Survey samples can be divided into two types, probability samples and non-probability samples. Probability-based samples implement a plan with specified probabilities. Probability-based sampling allows design-based inference about the target population, the inferences are based on a known objective probability distribution that was specified in the study protocol. Inferences from probability-based surveys may still suffer from many types of bias, surveys that are not based on probability sampling have greater difficulty measuring their bias or sampling error. Surveys based on non-probability samples often fail to represent the people in the target population, in academic and government survey research, probability sampling is a standard procedure. Any use of nonprobability sampling methods must be justified statistically and be able to measure estimation error, besides, random sampling and design-based inference are supplemented by other statistical methods, such as model-assisted sampling and model-based sampling. For example, many surveys have substantial amounts of nonresponse, even though the units are initially chosen with known probabilities, the nonresponse mechanisms are unknown. For surveys with substantial nonresponse, statisticians have proposed statistical models, issues related to survey sampling are discussed in several sources including Salant and Dillman. In a probability sample each member of the population has a known. For some target populations this process may be easy, for example, however, in large, disorganized populations simply constructing a suitable sample frame is often a complex and expensive task. Stratification is the process of dividing members of the population into homogeneous subgroups before sampling, the strata should be mutually exclusive, every element in the population must be assigned to only one stratum. The strata should also be collectively exhaustive, no element can be excluded. Then methods such as random sampling or systematic sampling can be applied within each stratum. This often improves the representativeness of the sample by reducing sampling error, Bias in surveys is undesirable, but often unavoidable
4.
Mathematical model
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A mathematical model is a description of a system using mathematical concepts and language. The process of developing a model is termed mathematical modeling. Mathematical models are used in the sciences and engineering disciplines. Physicists, engineers, statisticians, operations research analysts, and economists use mathematical models most extensively, a model may help to explain a system and to study the effects of different components, and to make predictions about behaviour. Mathematical models can take many forms, including systems, statistical models, differential equations. These and other types of models can overlap, with a model involving a variety of abstract structures. In general, mathematical models may include logical models, in many cases, the quality of a scientific field depends on how well the mathematical models developed on the theoretical side agree with results of repeatable experiments. Lack of agreement between theoretical mathematical models and experimental measurements often leads to important advances as better theories are developed, in the physical sciences, the traditional mathematical model contains four major elements. These are Governing equations Defining equations Constitutive equations Constraints Mathematical models are composed of relationships. Relationships can be described by operators, such as operators, functions, differential operators. Variables are abstractions of system parameters of interest, that can be quantified, a model is considered to be nonlinear otherwise. The definition of linearity and nonlinearity is dependent on context, for example, in a statistical linear model, it is assumed that a relationship is linear in the parameters, but it may be nonlinear in the predictor variables. Similarly, an equation is said to be linear if it can be written with linear differential operators. In a mathematical programming model, if the functions and constraints are represented entirely by linear equations. If one or more of the functions or constraints are represented with a nonlinear equation. Nonlinearity, even in simple systems, is often associated with phenomena such as chaos. Although there are exceptions, nonlinear systems and models tend to be difficult to study than linear ones. A common approach to nonlinear problems is linearization, but this can be if one is trying to study aspects such as irreversibility
5.
Country
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A country is a region that is identified as a distinct national entity in political geography. Sometimes the word countries is used to both to sovereign states and to other political entities, while other times it refers only to states. The word country comes from Old French contrée, itself derived from Vulgar Latin contrata and it most likely entered the English language after the Franco-Norman invasion during the 11th century. Areas much smaller than a state may be called by names such as the West Country in England, the Black Country, Constable Country. In many European countries the words are used for sub-divisions of the territory, as in the German Bundesländer. The modern Italian contrada is a word with its meaning varying locally, the term country is frequently used to refer to sovereign states. There is no agreement on the number of countries in the world. There are 206 sovereign states, of which 193 states are members of the United Nations, all are defined as states by declarative theory of statehood and constitutive theory of statehood. The latest proclaimed state is South Sudan in 2011, the Kingdom of Denmark, a sovereign state, comprises Metropolitan Denmark and two nominally separate countries—the Faroe Islands, and Greenland—which are almost fully internally self-governing. The Kingdom of the Netherlands, a state, comprises four separate countries, Netherlands, Aruba, Curaçao. The degree of autonomy of non-sovereign countries varies widely, some are possessions of sovereign states, as several states have overseas territories, with citizenry at times identical and at times distinct from their own
6.
Business
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A business is an organizational entity involved in the provision of goods and services to consumers. Businesses may also be social non-profit enterprises or state-owned public enterprises operated by governments with specific social, a business owned by multiple private individuals may form as an incorporated company or jointly organise as a partnership. Countries have different laws that may ascribe different rights to the business entities. The word business can refer to an organization or to an entire market sector or to the sum of all economic activity. Compound forms such as agribusiness represent subsets of the broader meaning. Businesses aim to maximize sales to have their income exceed their expenditures, resulting in a profit, the owner operates the business alone and may hire employees. A sole proprietor has unlimited liability for all obligations incurred by the business, partnership, A partnership is a business owned by two or more people. In most forms of partnerships, each partner has unlimited liability for the debts incurred by the business, the three most prevalent types of for-profit partnerships are, general partnerships, limited partnerships, and limited liability partnerships. Corporation, The owners of a corporation have limited liability and the business has a legal personality from its owners. Corporations can be either government-owned or privately owned and they can organize either for profit or as nonprofit organizations. A privately owned, for-profit corporation is owned by its shareholders, a privately owned, for-profit corporation can be either privately held by a small group of individuals, or publicly held, with publicly traded shares listed on a stock exchange. Cooperative, Often referred to as a co-op, a cooperative is a limited-liability business that can organize as for-profit or not-for-profit, a cooperative differs from a corporation in that it has members, not shareholders, and they share decision-making authority. Cooperatives are typically classified as either consumer cooperatives or worker cooperatives, cooperatives are fundamental to the ideology of economic democracy. In contrast, unincorporated businesses or persons working on their own are not as protected. Franchises, A franchise is a system in which entrepreneurs purchase the rights to open, franchising in the United States is widespread and is a major economic powerhouse. One out of retail businesses in the United States are franchised and 8 million people are employed in a franchised business. Real estate businesses sell, invest, construct and develop properties – including land, residential homes, retailers, wholesalers, and distributors act as middlemen and get goods produced by manufacturers to the intended consumers, they make their profits by marking up their prices. Most stores and catalog companies are distributors or retailers, transportation businesses such as railways, airlines, shipping companies that deliver goods and individuals to their destinations for a fee
7.
Clinical trial
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Clinical trials are experiments or observations done in clinical research. Clinical trials generate data on safety and efficacy and they are conducted only after they have received health authority/ethics committee approval in the country where approval of the therapy is sought. These authorities are responsible for vetting the risk/benefit ratio of the trial – their approval does not mean that the therapy is safe or effective, only that the trial may be conducted. Clinical trials can vary in size and cost, and they can involve a research center or multiple centers. Clinical study design aims to ensure the validity and reproducibility of the results. Trials can be costly, depending on a number of factors. The sponsor may be an organization or a pharmaceutical, biotechnology or medical device company. Certain functions necessary to the trial, such as monitoring and lab work, may be managed by an outsourced partner, only 10 percent of all drugs started in human clinical trials become an approved drug. Some clinical trials involve healthy subjects with no pre-existing medical conditions, other clinical trials pertain to patients with specific health conditions who are willing to try an experimental treatment. When participants are healthy volunteers who receive financial incentives, the goals are different than when the participants are sick, during dosing periods, study subjects typically remain under supervision for one to 40 nights. Usually pilot experiments are conducted to gain insights for design of the trial to follow. There are two goals to testing medical treatments, to whether they work well enough, called efficacy or effectiveness. The benefits must outweigh the risks, in the US, the elderly constitute only 14 percent of the population, while they consume over one-third of drugs. Women, children and people with unrelated medical conditions are frequently excluded. For women, a reason for exclusion is the possibility of pregnancy. If the sponsor cannot obtain enough test subjects at one location investigators at other locations are recruited to join the study, during the trial, investigators recruit subjects with the predetermined characteristics, administer the treatment and collect data on the subjects health for a defined time period. The researchers send the data to the sponsor, who then analyzes the pooled data using statistical tests. Except for small, single-location trials, the design and objectives are specified in a document called a clinical trial protocol
8.
Units of measurement
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A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same quantity. Any other value of quantity can be expressed as a simple multiple of the unit of measurement. For example, length is a physical quantity, the metre is a unit of length that represents a definite predetermined length. When we say 10 metres, we actually mean 10 times the definite predetermined length called metre, the definition, agreement, and practical use of units of measurement have played a crucial role in human endeavour from early ages up to this day. Different systems of units used to be very common, now there is a global standard, the International System of Units, the modern form of the metric system. In trade, weights and measures is often a subject of regulation, to ensure fairness. The International Bureau of Weights and Measures is tasked with ensuring worldwide uniformity of measurements, metrology is the science for developing nationally and internationally accepted units of weights and measures. In physics and metrology, units are standards for measurement of quantities that need clear definitions to be useful. Reproducibility of experimental results is central to the scientific method, a standard system of units facilitates this. Scientific systems of units are a refinement of the concept of weights, science, medicine, and engineering often use larger and smaller units of measurement than those used in everyday life and indicate them more precisely. The judicious selection of the units of measurement can aid researchers in problem solving, in the social sciences, there are no standard units of measurement and the theory and practice of measurement is studied in psychometrics and the theory of conjoint measurement. A unit of measurement is a quantity of a physical property. Units of measurement were among the earliest tools invented by humans, primitive societies needed rudimentary measures for many tasks, constructing dwellings of an appropriate size and shape, fashioning clothing, or bartering food or raw materials. Weights and measures are mentioned in the Bible and it is a commandment to be honest and have fair measures. As of the 21st Century, multiple unit systems are used all over the world such as the United States Customary System, the British Customary System, however, the United States is the only industrialized country that has not yet completely converted to the Metric System. The systematic effort to develop an acceptable system of units dates back to 1790 when the French National Assembly charged the French Academy of Sciences to come up such a unit system. After this treaty was signed, a General Conference of Weights, the CGPM produced the current SI system which was adopted in 1954 at the 10th conference of weights and measures. Currently, the United States is a society which uses both the SI system and the US Customary system
9.
International Standard Book Number
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The International Standard Book Number is a unique numeric commercial book identifier. An ISBN is assigned to each edition and variation of a book, for example, an e-book, a paperback and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, the method of assigning an ISBN is nation-based and varies from country to country, often depending on how large the publishing industry is within a country. The initial ISBN configuration of recognition was generated in 1967 based upon the 9-digit Standard Book Numbering created in 1966, the 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108. Occasionally, a book may appear without a printed ISBN if it is printed privately or the author does not follow the usual ISBN procedure, however, this can be rectified later. Another identifier, the International Standard Serial Number, identifies periodical publications such as magazines, the ISBN configuration of recognition was generated in 1967 in the United Kingdom by David Whitaker and in 1968 in the US by Emery Koltay. The 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108, the United Kingdom continued to use the 9-digit SBN code until 1974. The ISO on-line facility only refers back to 1978, an SBN may be converted to an ISBN by prefixing the digit 0. For example, the edition of Mr. J. G. Reeder Returns, published by Hodder in 1965, has SBN340013818 -340 indicating the publisher,01381 their serial number. This can be converted to ISBN 0-340-01381-8, the check digit does not need to be re-calculated, since 1 January 2007, ISBNs have contained 13 digits, a format that is compatible with Bookland European Article Number EAN-13s. An ISBN is assigned to each edition and variation of a book, for example, an ebook, a paperback, and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, a 13-digit ISBN can be separated into its parts, and when this is done it is customary to separate the parts with hyphens or spaces. Separating the parts of a 10-digit ISBN is also done with either hyphens or spaces, figuring out how to correctly separate a given ISBN number is complicated, because most of the parts do not use a fixed number of digits. ISBN issuance is country-specific, in that ISBNs are issued by the ISBN registration agency that is responsible for country or territory regardless of the publication language. Some ISBN registration agencies are based in national libraries or within ministries of culture, in other cases, the ISBN registration service is provided by organisations such as bibliographic data providers that are not government funded. In Canada, ISBNs are issued at no cost with the purpose of encouraging Canadian culture. In the United Kingdom, United States, and some countries, where the service is provided by non-government-funded organisations. Australia, ISBNs are issued by the library services agency Thorpe-Bowker
10.
Design of experiments
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The design of experiments is the design of any task that aims to describe or explain the variation of information under conditions that are hypothesized to reflect the variation. In its simplest form, an experiment aims at predicting the outcome by introducing a change of the preconditions, the change in the predictor is generally hypothesized to result in a change in the second variable, hence called the outcome variable. Main concerns in design include the establishment of validity, reliability. Related concerns include achieving appropriate levels of power and sensitivity. Correctly designed experiments advance knowledge in the natural and social sciences, other applications include marketing and policy making. In 1747, while serving as surgeon on HMS Salisbury, James Lind carried out a clinical trial to compare remedies for scurvy. This systematic clinical trial constitutes a type of DOE, Lind selected 12 men from the ship, all suffering from scurvy. Lind limited his subjects to men who were as similar as I could have them and he divided them into six pairs, giving each pair different supplements to their basic diet for two weeks. The treatments were all remedies that had proposed, A quart of cider every day. Twenty five gutts of vitriol three times a day upon an empty stomach, one half-pint of seawater every day. A mixture of garlic, mustard, and horseradish in a lump the size of a nutmeg, two spoonfuls of vinegar three times a day. Two oranges and one every day. The citrus treatment stopped after six days when they ran out of fruit, apart from that, only group one showed some effect of its treatment. The remainder of the crew served as a control. Charles S. Peirce randomly assigned volunteers to a blinded, repeated-measures design to evaluate their ability to discriminate weights, peirces experiment inspired other researchers in psychology and education, which developed a research tradition of randomized experiments in laboratories and specialized textbooks in the 1800s. Charles S. Peirce also contributed the first English-language publication on a design for regression models in 1876. A pioneering optimal design for regression was suggested by Gergonne in 1815. In 1918 Kirstine Smith published optimal designs for polynomials of degree six, herman Chernoff wrote an overview of optimal sequential designs, while adaptive designs have been surveyed by S. Zacks
11.
Scientific method
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The scientific method is a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. To be termed scientific, a method of inquiry is commonly based on empirical or measurable evidence subject to specific principles of reasoning, experiments need to be designed to test hypotheses. The most important part of the method is the experiment. The scientific method is a process, which usually begins with observations about the natural world. Human beings are naturally inquisitive, so often come up with questions about things they see or hear. The best hypotheses lead to predictions that can be tested in various ways, in general, the strongest tests of hypotheses come from carefully controlled and replicated experiments that gather empirical data. Depending on how well the tests match the predictions, the hypothesis may require refinement. If a particular hypothesis becomes very well supported a theory may be developed. Although procedures vary from one field of inquiry to another, identifiable features are shared in common between them. The overall process of the method involves making conjectures, deriving predictions from them as logical consequences. A hypothesis is a conjecture, based on knowledge obtained while formulating the question, the hypothesis might be very specific or it might be broad. Scientists then test hypotheses by conducting experiments, the purpose of an experiment is to determine whether observations agree with or conflict with the predictions derived from a hypothesis. Experiments can take anywhere from a college lab to CERNs Large Hadron Collider. There are difficulties in a statement of method, however. Though the scientific method is presented as a fixed sequence of steps. Not all steps take place in scientific inquiry, and are not always in the same order. Some philosophers and scientists have argued there is no scientific method, such as Lee Smolin. Nola and Sankey remark that For some, the idea of a theory of scientific method is yester-years debate
